DIscontinuous Noisy Active Meta I Composite MATERIALS

精心设计的结构可以形成一种有效的材料，其性质和功能在固体中是不寻常的;这种材料被称为超材料。机械超材料利用其构建块的弹性响应。传统上，超材料的性质不断变化，但最近出现了一类新的“不连续机械超材料”。到目前为止，大多数设计不连续机械超材料的尝试都集中在不同空间维度的变化行为上，但完全忽略了第四维-时间。然而，还已知的是，弹性突跳显示出复杂的动态行为。这个建议是关于如何利用弹性不稳定性的时间尺度来设计和驱动机械超材料，我们将寻求一个更好的定量理解的快速通过，从一个单一的元素到一个合奏的耦合单元电池，以及它的动力学是如何受到热波动的影响，我们希望这种理解可能会为设计新材料提供更有效的策略。这些数学模型将集中在细长固体，但也将是迈向更一般的，抽象的理论的行为不连续的超材料与相同的基本成分的弹性不稳定性的第一步。为了达到预期的目标，我们将利用该研究员在弹性不稳定性和统计力学方面的经验，以及导师在细长结构弹性变形数学建模方面的经验。该研究员将在牛津大学数学研究所工作。在Dominic Vella教授的指导下，该研究金将广泛拓宽研究员对动态细长结构和超材料数学模型的知识，以及其他补充科学技能。这一行动将大大有助于研究员的中期和长期职业发展。

Carefully architected structures can form an effective material whose properties and functionalities are unusual in solids; such materials are called metamaterials. Mechanical metamaterials harness the elastic response of their building blocks. Conventionally, a metamaterial's properties change continuously, but a new class of 'discontinuous mechanical metamaterials' have emerged recently. Thus far, most attempts to design discontinuous mechanical metamaterials have focussed on varying behaviour in different spatial dimensions but neglect the fourth dimension - time - altogether. However, it is also known that elastic snap-through shows intricate dynamic behaviour. This proposal is concerned with how the time scales of elastic instability can be harnessed for designing and actuating mechanical metamaterials.We will seek a better quantitative understanding of snap-through, from a single element to an ensemble of coupled unit cells, and how its dynamics is affected by thermal fluctuations; we expect that this understanding may give more effective strategies for designing new materials. These mathematical models will focus on slender solids but would also be a first step towards a more general, abstract theory of the behaviour of discontinuous metamaterials with the same basic ingredients of elastic instabilities. To meet the intended objectives, we will build on the fellow's experience in elastic instabilities and in statistical mechanics, and the supervisor's experience in the mathematical modelling of elastic deformation of slender structures.The fellow will be based in the Mathematical Institute of the University of Oxford. Under the supervision of Prof. Dominic Vella, the fellowship will extensively broaden the fellow's knowledge of the mathematical models of dynamic slender structures and metamaterials, together with other complementary scientific skills. This action will significantly contribute to the fellow's medium and long-term career development.